Koszul information geometry, Liouville-Mineur integrable systems and Moser isospectral deformation method for Hermitian positive-definite matrices

DOI10.1007/978-3-030-80209-7_39OpenAlexW3181474900MaRDI QIDQ2117870

Frédéric Barbaresco

Publication date: 22 March 2022

Full work available at URL: https://doi.org/10.1007/978-3-030-80209-7_39

zbMATH Keywords

information geometryLax pairsisospectral deformationcomplete integrable systems

Mathematics Subject Classification ID

Information theory (general) (94A15) Probability theory and stochastic processes (60-XX) Information geometry (statistical aspects) (62B11)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Completely integrable gradient systems on the manifolds of Gaussian and multinomial distributions
• Hereditary structure in Hamiltonians: Information geometry of Ising spin chains
• Hamiltonian group actions and integrable systems
• Completely integrable gradient flows
• Three integrable Hamiltonian systems connected with isospectral deformations
• Completely integrable Hamiltonian systems connected with semisimple Lie algebras
• Generalized Liouville method of integration of Hamiltonian systems
• Lax pair and fixed point analysis of Karmarkar's projective scaling trajectory for linear programming
• Neurodynamics and nonlinear integrable systems of Lax type
• Gradient systems associated with probability distributions
• On explicit solvable gradient systems of Moser-Karmarkar type
• Lax formalism for Gelfand-Tsetlin integrable systems
• Souriau exponential map algorithm for machine learning on matrix Lie groups
• Integrability and non-integrability in Hamiltonian mechanics
• Méthode de Le Verrier–Souriau et équations différentielles linéaires
• Stable and Random Motions in Dynamical Systems
• Integrable geodesic flows on homogeneous spaces
• Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
• A simple model of the integrable Hamiltonian equation
• On collective complete integrability according to the method of Thimm
• Lax–Nijenhuis operators for integrable systems

This page was built for publication: Koszul information geometry, Liouville-Mineur integrable systems and Moser isospectral deformation method for Hermitian positive-definite matrices